Problem Description

Obesity is rapidly becoming the scourge of the developed world due
to its strong correlation with many associated conditions including
coronary heart disease, ventricular dysfunction, congestive heart
failure, stroke, cardiac arrhythmias, metabolic syndrome, type II
diabetes, cardiovascular disease, sleep apnoea and osteoarthritis. In
the UK, 20–25% of adults are obese, with obesity in women and
men nearly tripling and quadrupling respectively between 1980 and
2002. The cost to the NHS in the year 2001–2 was approximately
£1bn.

Study Group Report

We have derived models for glucose and fat metabolism over these
timescales through glucagon and insulin production. Additional factors
which could be incorporated into this model are the distinction
between visceral fat and other fat stores, and the metabolism of
protein. Features which remain to be addressed include the calibration
of the model to parameter values from the literature, and
characterisation of factors such as lean body mass and number of
adipocytes which are agedependent and for which the model has a long
memory. These factors influence the evolution of fat levels and BMI
during puberty and through the rest of life. Mathematical problems
which we plan to address more rigorously in future work include a
rigorous averaging over the fast time scale to obtain a reduced model
for the long-time kinetics of fat-production. The model could easily
be extended to include factors such as appetite and insulin resistance
(through allowing gI to vary slowly in time).